Bayesian Analysis of Functions and Curves Using Registration

• Activity Number: 225
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Wen Cheng*+ and Ian L. Dryden and David Hitchcock and Xianzheng (Shan) Huang and Huiling Le
• Companies: and University of Nottingham and University of South Carolina and University of South Carolina-Columbia and University of Nottingham
• Keywords: Bayesian

Abstract

We consider Bayesian analysis of continuous functions and curves in 1D, 2D and 3D space. A fundamental aspect of the analysis is that it is invariant under a simultaneous warping of all the curves, as well as translation, rotation and scale of each individual. We consider Bayesian models based on the curve representation named the Square Root Velocity Function (SRVF) introduced by Srivastava et al. A Gaussian process model for the SRVF of curves is proposed, and suitable prior models such as Dirichlet process are employed for modeling the warping function as a Cumulative Distribution Function (CDF). Simulation from posterior distribution is via Markov chain Monte Carlo methods, and credibility regions for mean curves, warping functions as well as nuisance parameters are obtained. We will illustrate the methodology with applications in 1D proteomics data, 2D mouse vertebra outlines and 3D protein secondary structure element data.